You can choose from innumerable SMS apps on Android, including the one that came bundled with your phone. Microsoft has a new option... well, new to most of the world. It launched SMS Organizer a while back in India. After racking up more than a million downloads, the app has expanded globally.
SMS Organizer can send and receive text messages, but it's designed for use cases that don't exist in all countries. For example, it's common in India to access train schedules, account balances, appointment reminders, and more via SMS. SMS Organizer has a tabbed layout that makes all this easier to keep straight, and Microsoft promises it won't snoop on your personal data. You don't even need internet access because all the features work over SMS. If you do have internet access, the app can back up your message history to Google Drive.
The app is still technically "early access," so don't be surprised if there are bugs. You might also find most of the additional features of little use in your country. That said, there are plenty of places where SMS is as important as it is in India. If your SMS app just isn't cutting it, maybe SMS Organizer is the solution.